Wagdi G. Habashi

Eulerian modeling of supercooled large droplet splashing and bouncing

A conservative Eulerian numerical approach for modeling postimpact Supercooled Large Droplets undergoing splashing and bouncing on aircraft surfaces is presented. The approach introduces the effect of the postimpact droplets by successive solutions of the conservation equations. Two models have been selected to identify the droplet splashing and bouncing conditions, and to provide initial conditions for the reinjected water. The method has been applied to droplet impingement in Supercooled Large Droplet conditions on clean and iced NACA 23012 geometries, as well as the MS(1)-0317 airfoil, and the results have been compared to experimental data. Good agreement is observed for both impingement limits and collection efficiency. Additionally, the method has been applied to a three-element high-lift configuration operating in one of the proposed Appendixxa0O Supercooled Large Droplet environments to demonstrate the danger posed by the re-impingement of splashing and bouncing droplets on complex interacting aerod...

Simulation of Supercooled Large Droplet Impingement via Reduced Order Technology

A IRCRAFT flying through clouds of supercooled liquid droplets (SLD) can be subjected to in-flight ice accretion. Surface tension prevents the expansion of the droplets that would occur with phase change, forcing them to remain in liquid form even though their temperature is below the freezing point. When the droplets hit an aircraft’s surfaces, the surface tension decreases at the contact point, and theymay freeze completely on impact if the temperature is very low or freeze partially at higher temperatures, whereas the remaining liquid portion runs back on the surface, transported by the pressure gradient and the shear stress of the airflow. If no ice protection is provided, the aerodynamic characteristics of the aircraft and its handling can be severely degraded when ice accretes. The increased drag generated by the roughness of the ice can lead to flow separation, reduction of the stall margins, control reversals, and engine blockages [1]. Airworthiness of transport airplanes in icing conditions is demonstrated by compliance with certification standards (Appendix C of the FAA Federal Aviation Regulations, part 25) set by agencies, such as the Federal Aviation Administration, European Air Safety Association, Transport Canada, etc. These standards, frozen for 50 years, will soon undergo significant revisions with the adoption of Appendix O to address the icing threat posed by SLD conditions. Unlike smaller droplets, SLD can distort, break into smaller droplets, splash, bounce off surfaces, get carried downstream by the flow, and reimpinge, increasing the potential for ice contamination on unprotected surfaces [2–4]. Nowadays, wind tunnel tests, icing tunnel tests, and computer simulations play major complementary roles in the process of certifying a new aircraft [5,6]. Advances in modeling capabilities have created the conditions to accurately simulate the ice accretion process in a realistic three-dimensional (3-D) context [7,8]. Unfortunately, the computational cost associated with performing a multitude of 3-D simulations of various aeroicing conditions somewhat limits the widespread use of computational fluid dynamics (CFD), even if advanced computational resources are available [9,10]. To overcome this difficulty, mostly low-cost and, consequently, low-fidelity tools are usually employed. These may be based on empirical correlations, two-dimensional (2-D) approximations, inviscid or incompressible flow assumptions, and/or other simplifications that result in limited accuracy and realism. A viable alternative is the reduced-order modeling (ROM) approach [11,12], which dramatically reduces the cost of highfidelity simulations while providing solutions of superior accuracy to low-fidelity methods because it preserves the detailed physical modeling of the problem under consideration [13–16]. Although the use of this approach in the aeroicing environment is in its pioneering phase, recent results support the effectiveness of this methodology as a valuable tool in the context of a multicondition, multiparameter certification process [17–20]. In a framework of ice accretion simulation as the succession of airflow, water concentration, and heat transfer calculations, the most time-consuming part is obtaining the water impact patterns. The common practice is to assume a distribution of discrete droplet diameters, compute the impingement distribution of each diameter class, andweight-average thesemonodispersed solutions. In the case of the droplet sizes of Appendix C, seven distinct monodispersed sizes (Langmuir-D distribution) are used to compute the overall impingement distribution. In the SLD regime, however, due to the complex phenomena of droplet breakup, splashing, and bouncing, distributions containing up to 27 diameters of monodispersed droplets are needed to obtain realistic impingement predictions [5–7]. The computational cost of an SLD simulation is hence four times that of a Langmuir-D distribution. In the presentwork, it will be shown that the ROM approach can dramatically reduce cost with only a very modest degradation of the overall accuracy of the simulation. The essentials of the ROM approach used to extract the solution eigenfunctions (or modes) and compute solutions at unknown states are introduced in sections II and III of this paper, whereas section IV illustrates the interpolation technique used to compute the surrogate solutions. Finally, 2and 3-D results and comparison with experiments and other methods are presented to validate the present methodology. Received 29 July 2011; revision received 14 September 2011; accepted for publication 15 September 2011. Copyright

Development of a Jacobian-free finite element solver for aerothermodynamic design

Within the context of hypersonic flight, a finite element solver is introduced on the basis of a Jacobian-free implementation with the aim to address an arbitrary number of species with complex non-equilibrium thermodynamics in a computationally efficient and flexible manner. An adaptive edge-based formulation is proposed to define a general framework for the accurate solution of the conservation laws. Numerical and physical difficulties specific to high-speed flows are addressed for 2D and 3D cases.

Finite-Element Formulation of a Jacobian-free Solver for Supersonic Viscous Flows on Hybrid Grids

A parallel Jacobian-free solver for supersonic flows on unstructured hybrid meshes is proposed. An edge-based Finite Element formulation is used for spatial discretization with flow stabilized via either AUSM+-up or a Roe scheme. The Jacobian-free Newton-Krylov method is used as linear system solver and the lower-upper symmetric Gauss-Seidel method is used for matrix-free preconditioning. In the present formulation, second order approximations of spatial derivatives of the inviscid fluxes are introduced efficiently. Numerical results for Mach 1.93 flow past a sphere, Mach 4 flow past a waverider, and Mach 10.01 flow past a sphere, are presented.

Quasi-Unsteady Icing Simulation of an Oscillating Airfoil

Over the last two decades, steady-state and quasi-steady computational techniques have been proposed and used to model ice accretion on helicopter rotors in both hover and forward flight. These methods cannot accurately predict ice shapes or their aerodynamic impact on rotor performance, particularly in forward flight due to its unsteady nature. The current study proposes a methodology to predict ice accretion on oscillating airfoils with varying angles of attack. The computation of the airflow, droplet impingement, and ice accretion is carried out in an unsteady framework that preserves the characteristics of air, water droplets and ice accretion with respect to time. Application of this approach to an oscillating airfoil shows good agreement with experiments.

Finite element modeling of nonequilibrium fluid-wall interaction at high-Mach regime

The numerical modeling of the aerodynamic interactions at high-altitudes and high-Mach numbers is considered in view of its importance when studying problems where the continuum hypothesis at the f...

Ice accretion effects on helicopter rotor performance, via multibody and CFD approaches

A numerical approach for assessing the degraded aerodynamics and flight characteristics of ice-contaminated helicopter rotors is proposed. A hybrid two- and three-dimensional loose coupling strategy between Multibody Dynamics modeling and Computational Fluid Dynamics icing is formulated that attempts to balance computational resources, model complexity and accuracy for use during the early-design phases. A quasi-3D formulation that considers the heat transfer and the motion of the water film due to centrifugal effects is introduced. The method is suited for the analysis of rime, glaze and/or mixed ice conditions. Degraded aerodynamic and dynamic characteristics of the iced rotor and the changes in flight performance are assessed. The technique has been applied to the scenario of isolated helicopter rotors in hover and in forward flight. Deterioration of the figure of merit is also presented.

Modeling of large droplets impingement using a hybrid Taylor-Galerkin Variational Multi-Scale stabilized level set method

A Finite Element implementation of the Level Set method is coupled with an incompressible Navier-Stokes flow solver for the numerical modeling of water droplet dynamics for in-flight ice accretion. The proposed method adopts a hybrid second order Taylor-Galerkin Variational Multi-Scale stabilization approach for the Level Set equation, and a locally extended Finite Element approach for the Navier-Stokes equations. Various benchmark test cases are presented, including sloshing tank, Rayleigh-Taylor instability, and a rising bubble. The accuracy of the method is assessed and compared to other approaches available in literature.

Optimization of the Morphogenetic approach for in-flight icing

Recent improvements to the Morphogenetic approach, a Lagrangian stochastic ice accretion method, are presented. First, the mechanism of determining droplet impingement is redone in a way consistent with Eulerian droplet solvers, secondly, multi-shots have been enabled during the simulation process, and, finally, multiple mesh topologies have been enabled. The numerical method is evaluated for a NACA0012 airfoil and a GLC305 swept wing. In particular, the ability of the approach to simulate horns, feathers and of “lobster tails” or “scallops” is investigated. Numerical tests are performed to assess the accuracy of the proposed method and comparison with experimental data. An improvement in the shapes of ice is seen particularly at icing conditions where feathers are favored in two dimensions, and the lobster tails are expected to appear in three dimensions.